Yes. If one spouse decides to file for bankruptcy the other spouse isn’t forced to do so as well.
However, the spouse will be listed on the bankruptcy petition as a Non Filing Spouse, and usually that person’s income and debts will be listed on the bankruptcy petition. The Non Filing Spouse’s personal debts and credit score will not be affected.
Also, it is important to note that the bankruptcy of a spouse does not give a Non Filing Spouse the protection of the bankruptcy laws, i.e. the automatic stay and the bankruptcy discharge for debts that are in both spouses name.
Generally speaking, marriage doesn’t make both spouses personally liable for a debt. For example, only the spouse who signs a credit card agreement will be responsible for that debt. However, if both have signed such an agreement, and only one spouse files a bankruptcy, then the Non Filing Spouse will likely be held responsible for the debt.